Many viruses evolve rapidly. For example, haemagglutinin (HA) of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly emerged virus. In this paper, we use Shannon entropy and relative entropy to measure the diversity and selection pressure by an antibod...

Many viruses evolve rapidly. For example, hemagglutinin of the H3N2 influenza A virus evolves to escape antibody binding. This evolution of the H3N2 virus means that people who have previously been exposed to an influenza strain may be infected by a newly emerged virus. In this paper, we use Shannon entropy and relative entropy to measure the diversity and selection pressure by antibody in each...

We nd a lower bound for the entropy dissipation of the spatially homogeneous Landau equation with hard potentials in terms of the entropy itself. We deduce from this explicit estimates on the speed of convergence towards equilibrium for the solution of this equation. In the case of so-called overmaxwellian potentials, the convergence is exponential. We also compute a lower bound for the spectra...

This paper presents a new weighted entropy-based measure for assessing reliability of water distribution networks. The proposed methodology considers both of mechanical uncertainties (probability of pipe failure) and uncertainties due to hydraulic parameters (flow in pipe) simultaneously. In this methodology a penalty function is defined for different links of the network based on their probabi...

The Cross Entropy method is a well-known adaptive importance sampling method for rare-event probability estimation, which requires estimating an optimal importance sampling density within a parametric class. In this article we estimate an optimal importance sampling density within a wider semiparametric class of distributions. We show that this semiparametric version of the Cross Entropy method...

The Shannon entropy is a widely used summary statistic, for example, network traffic measurement, anomaly detection, neural computations, spike trains, etc. This study focuses on estimating Shannon entropy of data streams. It is known that Shannon entropy can be approximated by Rényi entropy or Tsallis entropy, which are both functions of the αth frequency moments and approach Shannon entropy a...

This paper treats different aspects of entropy measure in classical information theory and statistical quantum mechanics, it presents the possibility of extending the definition of Von Neumann entropy to image and array processing. In the first part, we generalize the quantum entropy using singular values of arbitrary rectangular matrices to measure the randomness and the quality of denoising o...

This chapter describes how difficult statistical estimation problems can often be solved efficiently by means of the cross-entropy (CE) method. The CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback–Leibler divergence as a measure of closeness between two sampling distributions. The CE method is particularly useful for the estimation of ...

In this paper, a rapid adaptive pedestrian detection method based on cascade classifier with ternary pattern is proposed. The proposed method achieves its goal by employing the following three new strategies: (1) A method for adjusting the key parameters of the trained cascade classifier dynamically for detecting pedestrians in unseen scenes using only a small amount of labeled data from the ne...

For playing the game of Tetris well, training a controller by the cross-entropy method seems to be a viable way (Szita and Lőrincz, 2006; Thiery and Scherrer, 2009). We consider this method to tune an evaluation-based one-piece controller as suggested by Szita and Lőrincz and we introduce some improvements. In this context, we discuss the influence of the noise, and we perform experiments with ...